Chapter 4.6, Problem 8G

A fun fact: you can use a microwave oven and a bar of chocolate to measure the speed of light. Really! Microwaves are electromagnetic waves, just like visible light. The difference is the wavelength of these waves: For visible light, the wavelengths are in the neighborhood of ${10}^{–6}$

m, while microwaves are close to ${10}^{–2}$

m. Basically, microwaves emitted in an oven make molecules in food vibrate, which causes heat. The first places to heat up are separated by half of a wavelength, so by using something that starts to melt visibly in certain spots, we can calculate the wavelength. We can then use that to calculate the speed of light, which I think we can all agree is pretty darn cool.

If your teacher is unusually adventurous, he or she might bring in a microwave and chocolate bars, in which case you can perform the experiment on your own. Start with around 20 seconds, and make sure you take out the carousel: the chocolate has to stay stationary. (And now you know why a lot of microwaves have a carousel: food heats more thoroughly at the spots corresponding to half of the wavelength.)

If no microwave and chocolate is available, I did the experiment at home and took a picture for you, which is reproduced here. It’s a life-size scale, so you can measure the distance between the melted spots with a ruler.

Find the error and relative error in your estimate as a decimal, and as a percentage. (If you need a refresher, relative difference was introduced in Lesson 2-4.) If your answer is WAY off, you might want to check the microwave to see if the frequency is different from 2.45 GHz.